In modern NMR instruments, nuclear spins are choreographed through application of RF pulses characterized by precision frequency, amplitude, phase, and inter-pulse delay interval as orchestrated by the pulse programmer, a functional block of software and communicating hardware. NMR measurement techniques are effectuated by RF pulse sequences, including sequences wherein the RF phase may be offset in different pulses. Successive pulses are specified in phase and duration with precise inter-pulse delays. Control of RF phase is achieved in one representative example of prior art as shown in FIG. 1 wherein the four phases of a period of a square wave are selectable from quadrant selector 110 from four sub-clocks 101-104, which track a master clock 100. Three DACs are required: DAC 112 having a 2 bit range, defines the quadrant, and the two DACs 114 and 116 (each typically 13 or 14 bit range), establish the vector component magnitudes in the selected quadrant. The vector sum of the outputs of DACs 114 and 116 is obtained with hybrid splitter 117 and combiners 118a, 118b and 118c to obtain the synthesized waveform. The multiple DACS of this phase synthesizer are burdensome for the assembly process, requiring careful attention to matching of correlative DACs. A transient problem may be encountered across the quadrant boundaries where phase transition continuity between quadrants is limited by the finite width phase step. Phase selective apparatus of this type has been incorporated in NMR apparatus supplied by Varian, Inc., Palo Alto, Calif. Prior art of the genre of FIG. 1 contains a multiplicity of components grouped to execute the functions of quadrant selection and RF amplitude selection within the selected quadrant.
In recent years, direct digital synthesis (DDR) has matured as a means for producing a desired analog waveform from a digital representation presented in the form of a sequence of digital words representing frequency, amplitude and phase information (“tuning words”) in accurate timed relationship as defined by a precise system clock. A central component for DDR apparatus is the digital to analog converter (DAC) which accepts a digital input and produces analog output. The quantization characteristic of the digital representation and the intrinsic nature of the input circuits will be reflected in the analog output without remediation of these patterns.
Physically recurrent waveforms are properly identified with a phase variable. The tuning word sequence should be regarded as containing sufficient information to fully describe amplitude, phase and spectral properties of the recurring periodic function. Discrete selection of the value of the phase variable is employed in NMR for a variety of purposes, such as detailed examination of intra-molecular couplings, as well as for the gross cancellation of phase dependent artifact in cyclic acquisitions. Phase has physical presence in NMR phenomena through the precession of nuclear spins about the polarizing (z direction) magnetic field. When a nuclear spin is tipped, e.g., the spin projection on the x-y plane is established, and the precessing component in the x-y (transverse) plane defines instantaneous phase in terms of a spatial coordinate. The NMR apparatus independently establishes a reference phase within the instrument in order that the manipulation of nuclear spins may be selected accurately with respect to the reference phase. Phase selection (or synthesis) defines a modulation envelope of selected duration and phase for the resonant RF pulse applied to a sample under study via NMR.
Direct digitally synthesized waveforms are now common in many digitally based instruments. Such synthesized waveforms are subject to anomalies such as phase errors, amplitude errors, and spurious frequency components. Errors originate from integral and differential non-linearities associated with digital to analog conversion (DAC) apparatus, and separately as an artifact of quantization. Rise and fall time, jitter and the like may contribute as well to undesirable performance. A contributing source of the quantization artifact derives from truncation of a mathematical element to accommodate the width of the tuning word as supplied to the DAC. The DAC itself contributes to a quantization error, because of its finite digital width, thereby constraining the dynamic range and precision of converted information. Discontinuities arising from the quantized signal, as processed by the digital-to-analog conversion are an obvious source of anomalous fourier components. It is known in the art to substantially ameliorate the latter in conversion from digital to analog representation by injecting a controlled amplitude increment of noise into the digital representation. This noise is typically of the order of the amplitude of the least significant bit (lsb) of the DAC. The practice is known as “dither” and can be generalized as an act of first perturbing a precise signal, followed by an averaging (or equivalent) operation on the now perturbed signal. The practice is discussed by many authorities, representative of which is the review of Vanderkooy and Lipshitz, J. (Audio Eng. Soc., v.32, No.3, 1984). It is known in prior art to combine noise perturbation, e.g., dither, with the phase angle coordinate, θ, or the function, f(θ). One specific example of prior art is suggested in “A Technical Tutorial on Digital Signal Synthesis”, p.93, (Analog Devices, Inc, 1994). In that reference, the noise increment is combined specifically with the phase coordinate. Limitation of injected noise to the phase coordinate is recognized in the present work to (theoretically) preserve the maximum dynamic range of the DAC when injected noise becomes appreciable, e.g., significantly larger than the least significant bit unit. Injection of non-band limited noise into the phase angle coordinate at increasing levels beyond the lsb unit of magnitude results in increasing noise in the recurrent (converted) waveform.
It should be observed that prior art has consistently emphasized amplitude fidelity in the synthesized signal with respect to the digital representation of the waveform. The phrase “phase synthesis” in the present work is intended to refer to the selection of an initial phase angle θ0 together with the evolving variable θi, (phase angle) continuing over the duration of an RF pulse derived from gating of the converted wave train.
It is known in other prior art to interpose a high pass filter between a noise generator and a tuning word (of the signal to be synthesized) in order to provide a source of filtered dither for DAC precision enhancement while minimizing the effect of introduced noise in the passband of the converted analog signal. The dither is further provided with means for noise amplitude adjustment to average over discontinuities introduced into the DAC transfer function in order to maintain linearity within specified limits. The provision therein for noise amplitude adjustment over an interval of at least as much as 23328 bits of an (effective) 16 bit DAC. Such maximum achievable dither amplitude is far in excess of the averaging interval required for the purpose of ameliorating intentionally introduced transfer function discontinuities. See Data Sheet, MB86060, 16 Bit Interpolating Digital to Analog Converter, Fujitsu Microelectronics. As a result of the choice of filtering in this particular prior art, the signal is restricted to the first Nyquist zone. The present work employs a more flexible digital filter to permit operation to occur in a selected, higher Nyquist zone. Consequently, a requirement for up-conversion of a first Nyquist zone filtered signal is obviated with clear savings in components.
In another specific instance of a dither enhanced DAC, it has been desired to remove the effect of the added noise in the DAC output through the artifice of a cancellation procedure. The digital signal (comprising a sequence of tuning words) is concurrently applied to one input of each of two combiners. A second input of each of the combiners receives the injected noise as a random or pseudo-random word which is presented in opposite sign to the respective combiners. Each combiner output communicates with a respective DAC and the analog outputs of the respective DACs are again combined to effect cancellation of noise artifact in these two sub-channels (U.S. Pat. No. 6,522,176). While this represents a technically elegant approach, it is apparent that the plurality of DACs increases the cost of production, not only in the cost of the second DAC, but also in the requirement for stable identical fidelity of the DACs to a common specification. Any departure from identical conversion performance simply introduces additional noise to the analog signal following the conversion operation.